Amauri Pereira de Oliveira Group of Micrometeorology Summer School Rio de Janeiro March 2009 3. PBL...
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Transcript of Amauri Pereira de Oliveira Group of Micrometeorology Summer School Rio de Janeiro March 2009 3. PBL...
Amauri Pereira de OliveiraGroup of
Micrometeorology
Summer SchoolRio de JaneiroMarch 2009
3. PBL MODELING
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Topics
1. Micrometeorology
2. PBL properties
3. PBL modeling
4. Modeling surface-biosphere interaction
5. Modeling Maritime PBL
6. Modeling Convective PBL
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Part 3
PBL MODELLING
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ModelModel is a tool used to simulate or forecast the behavior of a dynamic system.
Models are based on heuristic methods, statistics description, analytical or numerical solutions, simple physical experiments (analogical model). etc.
Dynamic system is a physical process (or set of processes) that evolves in time in which the evolution is governed by a set of physical laws.
Atmosphere is a dynamic system.
Model hereafter will always implies numerical model.
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Main modeling techniques
• Direct Numeric Simulation (DNS)
• Reynolds Averaged Navier-Stokes (RANS)
• Large Eddy Simulation (LES)
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DNS Model
• Numerical solution of the Navier-Stokes equation system.
• All scales of motion are solved.
• Does not have the closure problem.
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Kolmogorov micro scale.
l length scale of the most energetic eddies.
Scales of turbulence
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DNS model “grid dilemma”
• Number of grid points required for all length scales in a turbulent flow:
• PBL: Re ~ 107
• DNS requires huge computational effort even for small Re flow (~1000).
493 Re
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DNS Model
• First 3-D turbulence simulations (NCAR)
• First published DNS work was for isotropic turbulence Re = 35 in a grid of 323 (Orszag and Patterson, 1972)
• Nowadays: grid 10243
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Small resolved scale in the DNS model
Smallest length scale does not need to be the Kolmogorov microscale.
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Reynolds Number
How high should Re be?
There are situations where to increase Re means only to increase the sub-inertial interval.
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DNS Model – Final remarks
It has been useful to simulate properties of less complex non-geophysical turbulent flows
It is a very powerful tool for research of small Re flows (~ 1000)
The application of DNS model for Geophysical flow is is still incipient but very promising
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RANS Model
1. Diagnostic Model
2. Prognostic Model
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Closure Problem
Closure problem occurs when Reynolds average is applied to the equations of motion (Navier-Stoke).
The number of unknown is larger than the number of equations.
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Diagnostic RANS Model
Diagnostic RANS model are a set of the empirical expressions derived from the similarity theory valid for the PBL.
Zero order closure model
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PBL Similarity Theory
• Monin-Obukhov: Surface Layer (-1 < z/L < 1)
• Free Convection: Surface Layer ( z/L < -1)
• Mixing Layer Similarity: Convective PBL
• Local Similarity: Stable PBL
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Advantages
• Simplicity
• Yields variances and characteristic length scales required for air pollution dispersion modeling applications
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• Does not provide height of PBL
• Valid only for PBL in equilibrium
• Valid only for PBL over horizontally homogeneous surfaces
• Restrict to PBL layers and turbulence regimen of the similarity theories
Disadvantages
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Prognostic RANS model
• Mixing Layer Model (1/2 Order Closure)
• First Order Closure Model
• Second Order Closure Model
• 1.5 Order Closure Model
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Mixing Layer Model (1/2 Order Closure)
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Mixing Layer Model Hypothesis: turbulent mixing is strong enough to eliminate vertical gradients of mean thermodynamic (θ = Potential temperature) and dynamic properties in most of the PBL.
0z
M
bzaw
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Advantages
• Computational simplicity
• Yields a direct estimate of PBL height
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Disadvantages
• Restrict to convective conditions (Stable PBL very strong winds)
• Does not give information about variance of velocity or characteristic length scales
• Can only be applied to dispersion of pollutants in the cases when the pollutant is also well mixed in the PBL
First Order Closure Model
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First Order Closure Model
Are based on the analogy between turbulent and molecular diffusion.
λ is a characteristic length scale and u is a characteristic velocity scale.
z
uKwu M
Vertical flux
uK 1M
Diffusion coefficient
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First order closure model
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Advantage
• Computational simple
• Works fine for simple flow
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Disadvantage
• Requires the determination of the characteristic length and velocity scales
• It can not be applied for all regions and stability conditions present in the PBL (turbulence is a properties of the flow)
• It does not provide variances of the wind speed components
• It does not provide PBL height.
Second Order Closure Model
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Second Order Closure Model
SOCM are based on set of equations
that describe the first and second
order statistic moments and
parameterizing the third order terms.
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Reynolds Stress Tensor Equation
Molecular dissipation
Transport Tendency to isotropy
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Parametrization• Donaldson (1973)• Mellor and Yamada (1974)• André et al. (1978)• Mellor and Yamada (1982) • Therry and Lacarrére (1983)• Andrên (1990) • Abdella and MacFarlane
(1997) • Galmarini et al. (1998)• Abdella and MacFarlane
(2001)• Nakanishi (2001)• Vu et al. (2002)• Nakanishi and Niino (2004)
Based on laboratory experiments
Based on LES simulations
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TKE balance in the PBL
Stable
Convective
Destruição Térmica
Produção Térmica
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Advantages
•Provide a direct estimate of the PBL height.
•Provide a direct estimate of wind components variance.
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Disadvantages
•High computational cost
•Does not provide a direct estimate of the characteristic length scale
1.5 Order Closure Model
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1.5 Order closure model
• They are also based on the analogy between molecular and turbulent diffusion where the
• Turbulent diffusion coefficients are estimated in terms of the characteristic length and velocity scales
• Characteristic velocity scale is determined by resolving the TKE equation numerically
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z
eK
ze
ee
zK
g
z
v
z
uK
t
eM1
23
2H0
22
M
Turbulent kinetic energy (e) equation.
1.5 Order closure model
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Example of PBL structure simulated numerically during convective period using mesoscale model with a 1.5 order closure (Iperó, São Paulo, Brazil)
Cross section in the East-West direction
Iperó
Source: Pereira (2003)
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Advantages
• Moderate computational cost (mesoscale model)
• Provides a direct estimate of the PBL height
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One more equation to solve
Extra length scales to estimate
Does not provide a direct estimate of wind component variances
Disadvantages
LES Model
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LES Model
The motion equation are filtered in order
to describe only motions with a length
scale larger than a given threshold.
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Reynolds Average
f
)x('f)x(f)x(f
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LES Filter
)x(f)x(f~
)x(f
f
large eddies
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Convective Boundary Layer
Updraft
Source: Marques Filho (2004)
Cross section
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Convective PBL – LES Simulation
Source: Marques Filho (2004)
( zi /L ~ - 800)
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Spectral Properties – LES Simulation
Fonte: Marques Filho (2004)
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Advantages
Large scale turbulence is simulated
directly and sub grid (less dependent on
geometry flow) is parameterized.
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Disadvantages
Computational cost is high